On block-wise and reference panel-based estimators for genetic data prediction in high dimensions

TL;DR

This paper analyzes the effectiveness of block-wise and reference panel-based estimators for genetic prediction in high-dimensional data, revealing that local dependence adjustments may be less accurate than whole covariance methods, with performance varying based on data access.

Contribution

It provides a unified theoretical framework for evaluating block-wise and reference panel estimators in high-dimensional genetic prediction without sparsity assumptions.

Findings

Block-wise estimators can be less accurate than whole covariance estimators.

Performance of estimators varies significantly between training data and reference panels.

Theoretical results are supported by simulations and UK Biobank data analysis.

Abstract

Genetic prediction of complex traits and diseases has attracted enormous attention in precision medicine, mainly because it has the potential to translate discoveries from genome-wide association studies (GWAS) into medical advances. As the high dimensional covariance matrix (or the linkage disequilibrium (LD) pattern) of genetic variants has a block-diagonal structure, many existing methods attempt to account for the dependence among variants in predetermined local LD blocks/regions. Moreover, due to privacy restrictions and data protection concerns, genetic variant dependence in each LD block is typically estimated from external reference panels rather than the original training dataset. This paper presents a unified analysis of block-wise and reference panel-based estimators in a high-dimensional prediction framework without sparsity restrictions. We find that, surprisingly, even when the covariance matrix has a block-diagonal structure with well-defined boundaries, block-wise estimation methods adjusting for local dependence can be substantially less accurate than methods controlling for the whole covariance matrix. Further, estimation methods built on the original training dataset and external reference panels are likely to have varying performance in high dimensions, which may reflect the cost of having only access to summary level data from the training dataset. This analysis is based on our novel results in random matrix theory for block-diagonal covariance matrix. We numerically evaluate our results using extensive simulations and the large-scale UK Biobank real data analysis of 36 complex traits.